PRP Records

Probable Primes Top 10000

(183432 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
8001(29*10^57967+673)/957968Robert Price10/2017
8002(3^121492-5)/457966Lelio R Paula03/2012
80032^192549+3557964Lelio R Paula04/2011
800428799!2+257962Robert Price10/2012
8005(7*2^192534-1)/134757957Lelio R Paula01/2014
80067001^15069-10057943Enzo Doria07/2012
8007L(277273)/1109092157940Donovan Johnson11/2005
8008(2^192469-1017)/3557938Lelio R Paula02/2012
80092^192457-1155*19245757936Henri Lifchitz02/2005
80102^192443+138557932Lelio R Paula05/2011
8011132^27317-13157928Norbert Schneider03/2015
801241522!3-5904957912Robert Price12/2015
8013(3*2^192380-1)/16957911Lelio R Paula01/2014
80142^192339-251557900Yves Minet07/2014
80152^192303+769557889Lelio R Paula10/2012
80162^192273-595557880Lelio R Paula05/2011
80172^192257+1609557876Lelio R Paula05/2011
8018109^28401-257865Lelio R Paula10/2017
80192^192218-11186157864Enzo Doria05/2014
80202^192214-394157863Yves Minet04/2017
8021(2^192212+3)/25957860Lelio R Paula02/2012
8022(3^121270+8)/15593975357853Lelio R Paula03/2012
802380^30393-7957841Norbert Schneider03/2015
802420^44455-312357838Enzo Doria03/2013
80252^192122-19557835Lelio R Paula04/2011
8026(29*10^57834+91)/357835Robert Price03/2016
80278*6^74306+557823Lelio R Paula09/2014
8028(39^36341-1)/3857820Robert Price04/2012
80292^192037-11180557809Enzo Doria05/2014
80302^192023-192023^257805Henri Lifchitz05/2005
803121^43717+257804Ray Chandler08/2011
80328*5^82687+757797Lelio R Paula09/2014
80335^82680-2457791Lelio R Paula10/2012
8034(2^191915+47)/9557771Lelio R Paula02/2012
8035(74*10^57763+133)/957764Robert Price10/2017
80366^74227-9557760Lelio R Paula10/2012
80372^191861+2983557756Lelio R Paula10/2012
80391908^17605+17605^190857755Serge Batalov05/2014
80385*10^57754+5957755Robert Price09/2016
8040(5*2^191821-1)/892406757738Lelio R Paula01/2014
80413*8^63917+5^63917-3*4^63917+3*2^6391757724Mike Oakes11/2010
804241399!3-656157723Robert Price11/2015
80432^191745+1757721Lelio R Paula04/2011
80442^191730-76157717Yves Minet01/2012
8045(2^191733-3)/225157715Lelio R Paula02/2012
80462^191698-11157707Lelio R Paula04/2011
8047(13*10^57691+23)/957692Robert Price02/2015
804820^44340-542357688Enzo Doria03/2013
8049(27*2^191629+1)/12557686Lelio R Paula07/2012
80504*10^57684+3*7^5768457685Mike Oakes11/2010
80512*3^120898+557684Lelio R Paula04/2014
8052(6883*2^191610-1)/734757681Lelio R Paula04/2015
80536^74117-4957675Lelio R Paula10/2012
80542^191586-11320157674Enzo Doria07/2014
80552^191580+19357672Lelio R Paula04/2011
8056(103*29^39433+10401)/457669Curtis Bright05/2015
80572^191560+25525557666Lelio R Paula05/2011
80582^191515-8557652Lelio R Paula04/2011
80592^191502-112757648Yves Minet05/2013
80602*5^82473-3^8247357647Mike Oakes08/2010
8061(13*10^57634-61)/357635Robert Price08/2017
80622^191430+10357627Lelio R Paula04/2011
80633*2^191408+557621Lelio R Paula03/2014
80642^191382-185893157612Enzo Doria04/2016
80656*7^68163+557606Lelio R Paula09/2014
806691^29403-257602Lelio R Paula08/2013
806711^55308-795057598Enzo Doria02/2013
80682^191329+6557596Lelio R Paula04/2011
806911^55302-24057592Enzo Doria07/2012
80702^191299-103146757587Paul Bourdelais11/2012
80712^191295-11199157586Enzo Doria05/2014
80722^191279-129757581Yves Minet08/2012
80733*6^73961+557554Lelio R Paula09/2014
8074(3^120623+5)/5214457548Lelio R Paula04/2012
8075(17*10^57543-29)/357544Robert Price09/2017
807642^35445-4157537Norbert Schneider06/2014
8077(71^31079-1)/7057534Paul Bourdelais08/2017
80782^191069-72340357518Paul Bourdelais11/2012
80794*10^57506-357507Serge Batalov11/2010
808010^57501+6735957502Patrick De Geest06/2016
808110^57501-100000000157501Robert Price05/2016
808210^57501-24986157501Patrick De Geest06/2016
8083(9^60251+4^60251)/1357493Robert Price02/2013
808420^44184-600357485Enzo Doria03/2013
80852^190948+1270557482Lelio R Paula10/2012
80862^190945+2957481Henri Lifchitz06/2005
80872^190922-40157474Yves Minet01/2012
808815^48860+4657464Lelio R Paula02/2013
80893^120434+2057462Lelio R Paula10/2012
80907^67964-3857437Lelio R Paula10/2012
80912^190799-11306557437Enzo Doria07/2014
80929*5^82159+257428Lelio R Paula09/2014
8093(F(22898)^13-F(22897)^13)/F(22896)57422Wayne Halsdorf03/2012
8095lucasU(432,25,21787)-5*lucasU(432,25,21786)57416Mike Oakes05/2009
8094(103*10^57414-1)/357416Serge Batalov12/2014
8096(1654*30^38869-1)/2957416Karsten Bonath05/2017
80972*10^57410+9^5741057411Mike Oakes04/2011
80982^190704-159557408Lelio R Paula05/2011
809911^55121-174057403Enzo Doria11/2012
81002^190644-18557390Lelio R Paula04/2011
810141182!3-3^4118257389Robert Price08/2015
81022^190629-11225557386Enzo Doria06/2014
8103(2*10^57384-71)/357384Robert Price01/2017
81052*6^73735+5^7373557378Mike Oakes11/2009
81042^190605+5957378Lelio R Paula04/2011
81066^73727-757371Lelio R Paula10/2012
81072^190561-11222557365Enzo Doria06/2014
810810^57358+17089957359Patrick De Geest06/2016
810910^57358-800157358Robert Price03/2016
811018^45687-1157350Lelio R Paula02/2013
811111^55069-21057349Enzo Doria07/2012
811211^55068-1257348Lelio R Paula02/2013
811319^44839+5457339Lelio R Paula02/2013
8115(7*2^190468-1)/851157334Lelio R Paula01/2014
8114(23*10^57333-59)/957334Robert Price03/2017
81162^190455-1155*19045557333Henri Lifchitz02/2005
811765^31620+2857325Lelio R Paula01/2016
81182^190403+1609557318Lelio R Paula05/2011
8119(19*10^57316+119)/357317Robert Price02/2017
8120(21*2^190393+1)/21157314Lelio R Paula07/2012
81212^190392-11202557314Enzo Doria05/2014
8122(24737*2^190234+1)/957270Lelio R Paula05/2014
8123(7*2^190230+1)/2357265Lelio R Paula07/2012
8124(10223*2^190197+1)/321157256Lelio R Paula05/2014
812518^45590-9757228Lelio R Paula02/2013
8126(3*2^190105-1)/1920557224Lelio R Paula01/2014
8127(16*10^57219-31)/357220Robert Price03/2016
8128(2^190074+47)/5157217Lelio R Paula02/2012
81293^119894-14057204Lelio R Paula10/2012
8131(37^36473-1)/3657196Robert Price03/2012
81302^190000-216357196Yves Minet08/2013
81322^189987-279810757192Enzo Doria04/2016
81332^189935-11211757177Enzo Doria05/2014
81342^189909-11223157169Enzo Doria06/2014
8135132049#+14905357161Makoto Morimoto12/2015
813641032!3-2757158Robert Price09/2014
813719^44694+2257153Lelio R Paula02/2013
813812^52956-1757150Lelio R Paula02/2013
81392^189823-96757143Yves Minet01/2012
8140(25*10^57138-61)/957139Robert Price02/2015
81415^81743-4^(81743+1)57136Robert Price04/2016
81427^67593-5457123Lelio R Paula10/2012
81437*3^119712+257118Lelio R Paula03/2014
81445^81700+1657106Lelio R Paula10/2012
81452^189700+7656157106Enzo Doria05/2016
81462^189671+13157097Lelio R Paula04/2011
81474*6^73374+557097Lelio R Paula09/2014
8148(67607*2^189651+1)/4372757091Lelio R Paula05/2014
8149(29*2^189619-1)/39357080Lelio R Paula01/2014
81503^119587+8057058Lelio R Paula10/2012
81512^189502-11345357046Enzo Doria07/2014
81522^189455+15357032Lelio R Paula04/2011
815324^41317-41317^2457027Norbert Schneider07/2016
81542^189414-1757020Lelio R Paula03/2011
815524^41311+2357018Norbert Schneider12/2013
8156(4*10^56989-31)/956989Erik Branger05/2011
815711^54712-162056977Enzo Doria11/2012
81582^189237-11223156967Enzo Doria06/2014
815917^46285-4856952Lelio R Paula02/2013
81602^189188+7524156952Enzo Doria04/2016
81612^189181+9439556950Henri Lifchitz01/2005
81627001^14808-10856940Enzo Doria07/2012
81632^189147-11263956939Enzo Doria06/2014
81642^189110-356928M. Frind & P. Underwood11/2002
81652^189069+1290956916Lelio R Paula04/2011
8166(13*10^56909+191)/356910Robert Price08/2017
8167(35*10^56898-17)/956899Serge Batalov02/2009
81682^189011-595556898Lelio R Paula04/2011
81696^73119-556898Lelio R Paula10/2012
817013^51076-9056896Lelio R Paula02/2013
81712^188997+5689756894Yves Minet02/2010
81725^81388-1376656888Enzo Doria02/2013
817320^43713-640356872Enzo Doria03/2013
8174(71*10^56858-287)/956859Robert Price05/2017
81752^188857-25423356852Gary Barnes09/2009
817715^48338-8856850Lelio R Paula02/2013
817610^56849+13643756850Patrick De Geest07/2017
817810^56849-70156849Robert Price06/2017
8179(2^188788+78557)/356831Lelio R Paula05/2012
81802^188771+1609556826Lelio R Paula04/2011
81817*2^188742-956818Lelio R Paula03/2014
818212^52646-6556815Lelio R Paula02/2013
81835003^15358-15856813Enzo Doria07/2012
81842^188713+57729457556809Lelio R Paula03/2013
81852^188693-11209956803Enzo Doria05/2014
8186(7^67211+4^67211)/1156799Robert Price10/2012
81872^188678-9439556798Lelio R Paula09/2011
818820^43651-850356792Enzo Doria03/2013
81892^188657-237156792Yves Minet10/2013
8190(14^49549+5^49549)/1956789Robert Price05/2013
8191(45^34351-1)/4456788Robert Price05/2014
81927*10^56785-2356786Robert Price04/2016
8193(10^56781-31)/356781Serge Batalov12/2014
81947*10^56779+356780Erik Branger11/2009
819510^56765+25917956766Patrick De Geest09/2013
819610^56765-24949756765Patrick De Geest09/2013
8197t(188706)56764Robert Price04/2015
81982^188551-90432756760Paul Bourdelais11/2012
8199(64*10^56756+17)/956757Robert Price09/2015
8200131101#+14629156757Makoto Morimoto02/2016
82012^188539-11251956756Enzo Doria06/2014
82026^72927+10156749Lelio R Paula10/2012
820320^43617-160356748Enzo Doria03/2013
8204(3^118892-8)/9135892956718Lelio R Paula03/2012
8205(509203*2^188338-1)/356701Lelio R Paula03/2015
820620^43567-562356682Enzo Doria03/2013
82072^188234-11318356665Enzo Doria07/2014
8208(7*2^188215-1)/149731512556651Lelio R Paula01/2014
8209(1017*2^188171-1)/3556647Lelio R Paula03/2015
8210(34*10^56647-7)/9/37/26356644Makoto Morimoto04/2016
8211(2^188176-1017)/45381454356638Lelio R Paula02/2012
821233*10^56634+756636Robert Price07/2016
8214(F(31)^9241-F(30)^9241)/F(29)56634Wayne Halsdorf08/2010
821314^49413+3356634Lelio R Paula02/2013
82153^118680+11056625Lelio R Paula10/2012
8216(13*10^56624+161)/356625Robert Price04/2017
8217(3^118676-2)/751665326356613Lelio R Paula03/2012
8218(13*2^188062+1)/1756613Lelio R Paula07/2012
82192^188056-131356611Yves Minet08/2012
822020^43510-558356608Enzo Doria03/2013
82212^188032+1228556604Lelio R Paula03/2011
8222(265*10^56588+17)/356590Robert Price05/2016
82232^187959+577556582Lelio R Paula03/2011
8224(5*2^187959+1)/5356581Lelio R Paula07/2012
8225(11*2^187889-1)/35156559Lelio R Paula01/2014
8226(100049^11311+1)/10005056553Faysal YAtim09/2007
8227(19*10^56544-1)/956545Serge Batalov03/2009
822820^43447-892356526Enzo Doria03/2013
82292^187743-11217756517Enzo Doria06/2014
8230(F(5879)^47-F(5878)^47)/F(5877)56502Wayne Halsdorf08/2010
82315^80831-2256499Lelio R Paula10/2012
82325^80828-1316656497Enzo Doria02/2013
82337*2^187590-556472Lelio R Paula03/2014
82342^187555+7547356460Enzo Doria04/2016
82352^187541-28356456Yves Minet01/2012
8236(55*10^56453-1)/956454Serge Batalov03/2009
82372^187506-145156445Yves Minet08/2012
8238189^24794-256443Lelio R Paula10/2017
82396^72522+14356434Lelio R Paula10/2012
8240(15185*2^187452-1)/94956430Lelio R Paula03/2015
82412^187390+7956411Lelio R Paula03/2011
82422^187386+1290956409Lelio R Paula03/2011
82432^187382+61356408Jason Earls04/2008
8244(34*10^56392-7)/9/37/883/2388756384Makoto Morimoto04/2016
824520^43337-956383Lelio R Paula02/2013
8246(F(1008)^269-F(1007)^269)/F(1006)56364Wayne Halsdorf08/2010
82472^187230+42756362Henri Lifchitz01/2005
824811^54121-948056362Enzo Doria02/2013
8249(21*2^187202-1)/4356354Lelio R Paula01/2014
82502^187173-9156345Lelio R Paula03/2011


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: October, 17 2017 09:44 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!